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Info-gap forecasting and the advantage of sub-optimal models. (English) Zbl 1157.91427
Summary: We consider forecasting in systems whose underlying laws are uncertain, while contextual information suggests that future system properties will differ from the past. We consider linear discrete-time systems, and use a non-probabilistic info-gap model to represent uncertainty in the future transition matrix. The forecaster desires the average forecast of a specific state variable to be within a specified interval around the correct value. Traditionally, forecasting uses a model with optimal fidelity to historical data. However, since structural changes are anticipated, this is a poor strategy. Our first theorem asserts the existence, and indicates the construction, of forecasting models with sub-optimal-fidelity to historical data which are more robust to model error than the historically optimal model. Our second theorem identifies conditions in which the probability of forecast success increases with increasing robustness to model error. The proposed methodology identifies reliable forecasting models for systems whose trajectories evolve with Knightian uncertainty for structural change over time. We consider various examples, including forecasting European Central Bank interest rates following 9/11.

MSC:
91B84 Economic time series analysis
90B50 Management decision making, including multiple objectives
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[1] Bardsen, G.; Eitrheim, Ø.; Jansen, E.S.; Nymoen, R., The econometrics of macroeconomic modelling, (2005), Oxford University Press · Zbl 1089.91058
[2] Ben-Haim, Y., Art and the exponential: graphical exploration of the matrix exponential function, Leonardo, Journal of the international society for arts, (1997), Science s and Technology, 30, 49-52
[3] Ben-Haim, Y., Info-gap decision theory: decisions under severe uncertainty, (2006), Academic Press London
[4] Clements, M.P.; Hendry, D.F., Forecasting non-stationary economic time series, (1999), MIT Press · Zbl 0984.62069
[5] Hendry, D.F., Dynamic econometrics, (1995), Oxford University Press · Zbl 0897.62127
[6] Parker, E.N., Shielding space travelers, Scientific American, March, 41-47, (2006)
[7] Smith, D.J., Predictability and preparedness in influenza control, Science, 312, 392-394, (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.